Question

A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from $V$ to $32\,V$ the efficiency of the engine is

• A. 0.5
• B. 0.75
• C. 0.99
• D. 0.25

Answer 1

Answer: (B)

The efficiency of cycle is
$\eta = 1 - \frac{T_{2}}{T_{1}}$
for adiabatic process
$TV^{\gamma-1} =$ constant
For diatomic gas $\gamma = \frac{7}{5}$
$T_{1}V_{1}^{\gamma -1} = T_{2}V_{2}^{\gamma -1}$
$T_{1} = T_{2}\left(\frac{V_{2}}{V_{1}}\right)^{\gamma-1}$
$T_{1} = T_{2} \left(35\right)^{\frac{7}{5}-1}$
$= T_{2}\left(2^{5}\right)^{2/ 5}$
$= T_{2} \times 4$
$T_{1} = 4T_{2}.$
$\eta = \left(1-\frac{1}{4}\right) = \frac{3}{4} = 0.75$